Abstract
In a structural matrix ring Mn (ρ R) over an arbitrary ring R we determine the centralizer of the set of matrix units in Mn (ρR) associated with the anti-symmetric part of the reflexive and transitive binary relation ρ on {1,2,…,n}. If the underlying ring R has no proper essential ideal, for example if R is a field, then we show that the largest ideal of Mn (ρR) contained in the mentioned centralizer coincides with the smallest essential ideal of Mn (ρR).
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